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    Question

    A vessel contains a mixture of milk and water in the

    ratio 3: 2. If 10 liters of the mixture are taken out and replaced with 10 liters of water, the ratio of milk to water becomes 2: 3. What is the total volume of the mixture in the vessel?
    A 20 Correct Answer Incorrect Answer
    B 25 Correct Answer Incorrect Answer
    C 30 Correct Answer Incorrect Answer
    D 35 Correct Answer Incorrect Answer
    E 40 Correct Answer Incorrect Answer

    Solution

    Let the total volume of the mixture be 5x liters (since the ratio is 3: 2).  Initially, quantity of milk = 3x liters, and water = 2x liters.  After removing 10 liters of the mixture and adding 10 liters of water:  Milk left = 3x - 6 liters.  Water left = 2x + 6 liters.  New ratio = (3x – 6): (2x + 6) = 2: 3.  Cross-multiplying and solving:  9x - 18 = 4x + 12  5x = 30  x = 6  Total volume of the mixture = 5x = 30 liters.

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